Just because you start talking doesn't mean that someone is listening.
Things to look for:
1) Watch their body language (are they paying attention?, are they reading? looking off into the distance? have a scowl on their face? folded arms, tapping their foot?).
2) Do they try to interrupt you with their own statements, comments, questions or observations, as if they didn't hear you?
3) When they respond: did they listen to your statements, comments, questions or observations? or do they respond as if they were thinking about their response while you were talking and complete ignored the last half of what you said?
4) Do they try to change to focus/topic of the conversation to divert your attention so they don't have to answer for some transgression? Do they attempt to turn the conversation back on you and get you to try and defend yourself?
What you can do:
1) Stop talking and ask them what problems they are having with what you are saying?
2) Ask them to let you finish your thoughts before they start talking. You'll do the same for them.
3) Ask them to repeat what was said or their understanding of what was said.
4) Repeat your thoughts briefly and ask them to respond directly. If they don't respond directly, ask them why.
5) When the other party makes observations, comments, statement or ask questions, ask them what the basis is for their thoughts. "Why are you asking me that?" Why is it important? Why is it important to you?
If you don't want to answer, politely decline. That's your right, same as it's their right to speak out and comment or question. Free speech works both ways.
6) If the conversation does go into a different direction, you can make a mental note or even state verbally that you'll get back to the main topic. Or you can ask that the new topic be deferred until the current topic is resolved.
7) If others want to express themselves freely but want you to restrict your comments, questions, observations and statements, you'll see it, point it out and then respond accordingly. Ask them why they don't want to listen to you. I have seen this many times where someone calls on the phone, goes into a rant, then when the listener starts talking, all of a sudden, the caller has to go. Sometimes they really do have to go, most of the time, IME, they really don't want to hear what you have to say because they just wanted to dump on you to get their anger out and once that's done, they move on, leaving you with all the crap they just let go of. If it happens more than once, call them on it and next time, politely tell them you have to go and next time lets talk about something else other than the callers problems. See how they respond then. React accordingly.
For all of the above, I suggest you remain calm, cool, and collected. It will drive high anxiety people nuts and allow them to show their true selves. For other people who appreciate civility, it will reinforce the notion that you are someone who can carry on a productive discussion.
Respond accordingly.
It takes some practice to get all the above in your brain to the point of actually being aware of what's happening in real time. Mindfullness is a state of being that has many proponents. With time and practice, awareness becomes second nature.
There are many books written on this stuff but this is how I conceptualize these type of situations for myself. YMMV